On a Number Pyramid Related to the Binomial, Deleham, Eulerian, MacMahon and Stirling number triangles

dc.contributor.author	Franssens, G.R.
dc.date	2006
dc.date.accessioned	2016-11-22T12:47:49Z
dc.date.available	2016-11-22T12:47:49Z
dc.identifier.uri	https://orfeo.belnet.be/handle/internal/4509
dc.description	We study a particular number pyramid bn,k,l that relates the binomial, Deleham, Eulerian, MacMahon-type and Stirling number triangles. The numbers bn,k,l are generated by a function Bc(x, y, t), c ∈ ℂ, that appears in the calculation of derivatives of a class of functions whose derivatives can be expressed as polynomials in the function itself or a related function. Based on the properties of the numbers b n,k,l, we derive several new relations related to these triangles. In particular, we show that the number triangle Tn,k, recently constructed by Deleham (Sloane's A088874), is generated by the Maclaurin series of sechct, c ∈ ℂ. We also give explicit expressions and various partial sums for the triangle Tn,k. Further, we find that e2pm, the numbers appearing in the Maclaurin series of coshm t, for all m ∈ ℕ, equal the number of closed walks, based at a vertex, of length 2p along the edges of an m-dimensional cube.
dc.language	eng
dc.title	On a Number Pyramid Related to the Binomial, Deleham, Eulerian, MacMahon and Stirling number triangles
dc.type	Article
dc.subject.frascati	Mathematics
dc.audience	Scientific
dc.source.title	Journal of Integer Sequences
dc.source.volume	9
dc.source.issue	4
dc.source.page	1-34
Orfeo.peerreviewed	Yes
dc.identifier.scopus	2-s2.0-33747689079